Light falls on two slits spaced 0.19 mm apart. If the angle between the first dark fringe and the central maximum is 0.047°, what is the wavelength of the light?

Question

Light falls on two slits spaced 0.19 mm apart. If the angle between the first dark fringe and the central maximum is 0.047°, what is the wavelength of the light?

Answer 1

For the dark fringes, you use

d sinθ = (n – 0.5) λ where n=1,2,3,4 ...

So, for the first dark fringe we use n=1. This leads us to

(0.19) sin(0.047^o) = (0.5) λ ⇒ λ = 0.0003117 mm = 311.7 nm